Colloidal metal labeling systems are utilized in high-resolution electron microscopic studies of biological structure and ultrastructure. The small nanometer sized collidal conjugates are used to identify and localize specific molecular and sub-molecular elements. Currently studies are empirical and rely on estimates to select labeling parameters. Maximal efficiency of labeling depends on a number of factors including label concentration, label size, temperature, and other properties of the labeling media. Also important are the affinities of the colloid-conjugated antibody or ligand for their respective antigen or receptor, target accessibility, and the fluid flow imposed during labeling. In certain applications involving living cells it is desirable to minimize the labeling time. It is critical that investigators be able to choose optimal labeling conditions. This is particularly important when quantitative or co-localization studies that involve simultaneous multiple labels of different metal composition, shape, or size are employed. The proposed collaborative studies involve an applied mathematics group and a biology group with substantial expertise in the development and use of colloidal labeling systems. Mathematical models will be developed and tested in order to maximize the efficiency and accuracy of labeling in a variety of conditions commonly encountered in the labeling of biological systems. Mathematical models developed for the colloidal labeling systems are very similar in form to models, which describe certain optical biosensor systems such as the BIAcore and IAsys. Mathematical models developed for the colloidal labeling systems will be applied to the refinement of biosensor model systems. Beyond the specific applications, all biological processes occur within the colloidal regime. A substantially improved understanding of the more simplified colloidal interactions involved in labeling may ultimately be important in the understanding of a wide variety of biological questions.